%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : NUM545+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n015.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 27 08:17:21 AM UTC 2026
% Result : Theorem 5.23s 1.15s
% Output : CNFRefutation 5.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 12
% Syntax : Number of formulae : 62 ( 23 unt; 0 def)
% Number of atoms : 167 ( 23 equ)
% Maximal formula atoms : 15 ( 2 avg)
% Number of connectives : 178 ( 73 ~; 71 |; 22 &)
% ( 3 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 58 ( 1 sgn 27 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(mDefEmp,axiom,
! [W0] :
( W0 = slcrc0
<=> ( ~ ? [W1] : aElementOf0(W1,W0)
& aSet0(W0) ) ),
file('theBenchmark.p',mDefEmp) ).
fof(mDefSub,axiom,
! [W0] :
( aSet0(W0)
=> ! [W1] :
( aSubsetOf0(W1,W0)
<=> ( ! [W2] :
( aElementOf0(W2,W1)
=> aElementOf0(W2,W0) )
& aSet0(W1) ) ) ),
file('theBenchmark.p',mDefSub) ).
fof(mSubRefl,axiom,
! [W0] :
( aSet0(W0)
=> aSubsetOf0(W0,W0) ),
file('theBenchmark.p',mSubRefl) ).
fof(mSubTrans,axiom,
! [W0,W1,W2] :
( ( aSet0(W2)
& aSet0(W1)
& aSet0(W0) )
=> ( ( aSubsetOf0(W1,W2)
& aSubsetOf0(W0,W1) )
=> aSubsetOf0(W0,W2) ) ),
file('theBenchmark.p',mSubTrans) ).
fof(mNATSet,axiom,
( isCountable0(szNzAzT0)
& aSet0(szNzAzT0) ),
file('theBenchmark.p',mNATSet) ).
fof(mSuccNum,axiom,
! [W0] :
( aElementOf0(W0,szNzAzT0)
=> ( szszuzczcdt0(W0) != sz00
& aElementOf0(szszuzczcdt0(W0),szNzAzT0) ) ),
file('theBenchmark.p',mSuccNum) ).
fof(mDefMax,axiom,
! [W0] :
( ( W0 != slcrc0
& isFinite0(W0)
& aSubsetOf0(W0,szNzAzT0) )
=> ! [W1] :
( W1 = szmzazxdt0(W0)
<=> ( ! [W2] :
( aElementOf0(W2,W0)
=> sdtlseqdt0(W2,W1) )
& aElementOf0(W1,W0) ) ) ),
file('theBenchmark.p',mDefMax) ).
fof(m__1986,axiom,
( isFinite0(xS)
& aSubsetOf0(xS,szNzAzT0) ),
file('theBenchmark.p',m__1986) ).
fof(m__2035,axiom,
( xS != slcrc0
=> aSubsetOf0(xS,slbdtrb0(szszuzczcdt0(szmzazxdt0(xS)))) ),
file('theBenchmark.p',m__2035) ).
fof(m__,conjecture,
? [W0] :
( aSubsetOf0(xS,slbdtrb0(W0))
& aElementOf0(W0,szNzAzT0) ),
file('theBenchmark.p',m__) ).
fof(m___neg,negated_conjecture,
~ ? [W0] :
( aSubsetOf0(xS,slbdtrb0(W0))
& aElementOf0(W0,szNzAzT0) ),
inference(assume_negation,[status(cth)],[m__]) ).
cnf(c_55,negated_conjecture,
( ~ aSubsetOf0(xS,slbdtrb0(A))
| ~ aElementOf0(A,szNzAzT0) ),
inference(clausify,[status(thm)],[m___neg]) ).
cnf(c_56,plain,
( aSubsetOf0(xS,slbdtrb0(szszuzczcdt0(szmzazxdt0(xS))))
| xS = slcrc0 ),
inference(clausify,[status(thm)],[m__2035]) ).
cnf(c_57,plain,
isFinite0(xS),
inference(clausify,[status(thm)],[m__1986]) ).
cnf(c_58,plain,
aSubsetOf0(xS,szNzAzT0),
inference(clausify,[status(thm)],[m__1986]) ).
fof(mSegZero,axiom,
slbdtrb0(sz00) = slcrc0,
file('theBenchmark.p',mSegZero) ).
cnf(c_64,plain,
slbdtrb0(sz00) = slcrc0,
inference(clausify,[status(thm)],[mSegZero]) ).
cnf(c_65,plain,
slcrc0 = slbdtrb0(sz00),
inference(copy,[status(thm)],[c_64]) ).
cnf(c_78,plain,
( aElementOf0(B,A)
| szmzazxdt0(A) != B
| slcrc0 = A
| ~ isFinite0(A)
| ~ aSubsetOf0(A,szNzAzT0) ),
inference(clausify,[status(thm)],[mDefMax]) ).
cnf(c_108,plain,
( aElementOf0(szszuzczcdt0(A),szNzAzT0)
| ~ aElementOf0(A,szNzAzT0) ),
inference(clausify,[status(thm)],[mSuccNum]) ).
fof(mZeroNum,axiom,
aElementOf0(sz00,szNzAzT0),
file('theBenchmark.p',mZeroNum) ).
cnf(c_109,plain,
aElementOf0(sz00,szNzAzT0),
inference(clausify,[status(thm)],[mZeroNum]) ).
cnf(c_111,plain,
aSet0(szNzAzT0),
inference(clausify,[status(thm)],[mNATSet]) ).
cnf(c_136,plain,
( aSubsetOf0(A,C)
| ~ aSubsetOf0(B,C)
| ~ aSubsetOf0(A,B)
| ~ aSet0(C)
| ~ aSet0(B)
| ~ aSet0(A) ),
inference(clausify,[status(thm)],[mSubTrans]) ).
cnf(c_138,plain,
( aSubsetOf0(A,A)
| ~ aSet0(A) ),
inference(clausify,[status(thm)],[mSubRefl]) ).
fof(nnf_9,plain,
! [W0] :
( ! [W1] :
( ( ? [W2] :
( ~ aElementOf0(W2,W0)
& aElementOf0(W2,W1) )
| ~ aSet0(W1)
| aSubsetOf0(W1,W0) )
& ( ( ! [X0] :
( aElementOf0(X0,W0)
| ~ aElementOf0(X0,W1) )
& aSet0(W1) )
| ~ aSubsetOf0(W1,W0) ) )
| ~ aSet0(W0) ),
inference(fof_nnf,[status(thm)],[mDefSub]) ).
fof(sk_mDefSub_sk,plain,
! [W0] :
( ! [W1] :
( ( ( ~ aElementOf0(sK0(W0,W1),W0)
& aElementOf0(sK0(W0,W1),W1) )
| ~ aSet0(W1)
| aSubsetOf0(W1,W0) )
& ( ( ! [X0] :
( aElementOf0(X0,W0)
| ~ aElementOf0(X0,W1) )
& aSet0(W1) )
| ~ aSubsetOf0(W1,W0) ) )
| ~ aSet0(W0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(W2,sK0(W0,W1))],[nnf_9]) ).
fof(sk_mDefSub,plain,
( ! [VAR_0,VAR_1] :
( ~ aElementOf0(sK0(VAR_0,VAR_1),VAR_0)
| ~ aSet0(VAR_1)
| aSubsetOf0(VAR_1,VAR_0)
| ~ aSet0(VAR_0) )
& ! [VAR_0,VAR_1] :
( aElementOf0(sK0(VAR_0,VAR_1),VAR_1)
| ~ aSet0(VAR_1)
| aSubsetOf0(VAR_1,VAR_0)
| ~ aSet0(VAR_0) )
& ! [VAR_0,VAR_1,VAR_2] :
( aElementOf0(VAR_2,VAR_0)
| ~ aElementOf0(VAR_2,VAR_1)
| ~ aSubsetOf0(VAR_1,VAR_0)
| ~ aSet0(VAR_0) )
& ! [VAR_0,VAR_1] :
( aSet0(VAR_1)
| ~ aSubsetOf0(VAR_1,VAR_0)
| ~ aSet0(VAR_0) ) ),
inference(cnf_transformation,[status(thm)],[sk_mDefSub_sk]) ).
cnf(c_141,plain,
( aElementOf0(sK0(A,B),B)
| ~ aSet0(B)
| aSubsetOf0(B,A)
| ~ aSet0(A) ),
inference(split_conjunct,[status(thm)],[sk_mDefSub]) ).
cnf(c_142,plain,
( aElementOf0(C,A)
| ~ aElementOf0(C,B)
| ~ aSubsetOf0(B,A)
| ~ aSet0(A) ),
inference(split_conjunct,[status(thm)],[sk_mDefSub]) ).
cnf(c_143,plain,
( aSet0(B)
| ~ aSubsetOf0(B,A)
| ~ aSet0(A) ),
inference(split_conjunct,[status(thm)],[sk_mDefSub]) ).
cnf(c_148,plain,
( ~ aElementOf0(B,A)
| slcrc0 != A ),
inference(clausify,[status(thm)],[mDefEmp]) ).
cnf(c_149,plain,
( aSet0(A)
| slcrc0 != A ),
inference(clausify,[status(thm)],[mDefEmp]) ).
cnf(c_168,plain,
( ~ aElementOf0(szszuzczcdt0(szmzazxdt0(xS)),szNzAzT0)
| xS = slcrc0 ),
inference(resolve,[status(thm)],[c_56,c_55]) ).
cnf(c_2445,plain,
( aElementOf0(A,xS)
| szmzazxdt0(xS) != A
| slcrc0 = xS
| ~ isFinite0(xS) ),
inference(resolve,[status(thm)],[c_78,c_58]) ).
cnf(c_2446,plain,
( aElementOf0(A,xS)
| szmzazxdt0(xS) != A
| xS = slcrc0
| ~ isFinite0(xS) ),
inference(copy,[status(thm)],[c_2445]) ).
cnf(c_172,plain,
( aElementOf0(A,xS)
| szmzazxdt0(xS) != A
| xS = slcrc0 ),
inference(resolve,[status(thm)],[c_57,c_2446]) ).
cnf(c_199,negated_conjecture,
~ aSubsetOf0(xS,slbdtrb0(sz00)),
inference(resolve,[status(thm)],[c_55,c_109]) ).
cnf(c_2447,plain,
( aElementOf0(A,szNzAzT0)
| ~ aElementOf0(A,xS)
| ~ aSet0(szNzAzT0) ),
inference(resolve,[status(thm)],[c_142,c_58]) ).
cnf(c_226,plain,
( aElementOf0(A,szNzAzT0)
| ~ aElementOf0(A,xS) ),
inference(resolve,[status(thm)],[c_111,c_2447]) ).
cnf(c_2448,plain,
( aSet0(xS)
| ~ aSet0(szNzAzT0) ),
inference(resolve,[status(thm)],[c_143,c_58]) ).
cnf(c_228,plain,
aSet0(xS),
inference(resolve,[status(thm)],[c_111,c_2448]) ).
cnf(c_251,plain,
aSet0(slbdtrb0(sz00)),
inference(resolve,[status(thm)],[c_149,c_65]) ).
cnf(c_252,plain,
aSet0(slcrc0),
inference(xxres,[status(thm)],[c_149]) ).
cnf(c_266,plain,
( aElementOf0(sK0(A,xS),xS)
| aSubsetOf0(xS,A)
| ~ aSet0(A) ),
inference(resolve,[status(thm)],[c_228,c_141]) ).
cnf(c_276,plain,
aSubsetOf0(slcrc0,slcrc0),
inference(resolve,[status(thm)],[c_252,c_138]) ).
cnf(c_308,plain,
( aElementOf0(szmzazxdt0(xS),xS)
| xS = slcrc0 ),
inference(xxres,[status(thm)],[c_172]) ).
cnf(c_320,plain,
aSubsetOf0(slcrc0,slbdtrb0(sz00)),
inference(paramod,[status(thm)],[c_65,c_276]) ).
cnf(c_2449,plain,
( aSubsetOf0(xS,B)
| ~ aSubsetOf0(A,B)
| ~ aSubsetOf0(xS,A)
| ~ aSet0(B)
| ~ aSet0(A) ),
inference(resolve,[status(thm)],[c_136,c_228]) ).
cnf(c_2450,plain,
( aSubsetOf0(xS,A)
| ~ aSubsetOf0(slcrc0,A)
| ~ aSubsetOf0(xS,slcrc0)
| ~ aSet0(A) ),
inference(resolve,[status(thm)],[c_2449,c_252]) ).
cnf(c_2451,plain,
( aSubsetOf0(xS,slbdtrb0(sz00))
| ~ aSubsetOf0(slcrc0,slbdtrb0(sz00))
| ~ aSubsetOf0(xS,slcrc0) ),
inference(resolve,[status(thm)],[c_2450,c_251]) ).
cnf(c_2452,plain,
( aSubsetOf0(xS,slbdtrb0(sz00))
| ~ aSubsetOf0(xS,slcrc0) ),
inference(resolve,[status(thm)],[c_2451,c_320]) ).
cnf(c_744,plain,
~ aSubsetOf0(xS,slcrc0),
inference(resolve,[status(thm)],[c_2452,c_199]) ).
cnf(c_2453,plain,
( aElementOf0(sK0(slcrc0,xS),xS)
| aSubsetOf0(xS,slcrc0) ),
inference(resolve,[status(thm)],[c_266,c_252]) ).
cnf(c_1772,plain,
aElementOf0(sK0(slcrc0,xS),xS),
inference(resolve,[status(thm)],[c_744,c_2453]) ).
cnf(c_2454,plain,
slcrc0 != xS,
inference(resolve,[status(thm)],[c_1772,c_148]) ).
cnf(c_1783,plain,
xS != slcrc0,
inference(copy,[status(thm)],[c_2454]) ).
cnf(c_1852,plain,
aElementOf0(szmzazxdt0(xS),xS),
inference(resolve,[status(thm)],[c_1783,c_308]) ).
cnf(c_1867,plain,
~ aElementOf0(szszuzczcdt0(szmzazxdt0(xS)),szNzAzT0),
inference(resolve,[status(thm)],[c_1783,c_168]) ).
cnf(c_2239,plain,
aElementOf0(szmzazxdt0(xS),szNzAzT0),
inference(resolve,[status(thm)],[c_1852,c_226]) ).
cnf(c_2455,plain,
aElementOf0(szszuzczcdt0(szmzazxdt0(xS)),szNzAzT0),
inference(resolve,[status(thm)],[c_2239,c_108]) ).
cnf(c_2444,plain,
$false,
inference(resolve,[status(thm)],[c_1867,c_2455]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM545+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n015.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sat Sep 26 03:14:12 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.36 % Process 2983854 was started by sandbox on n015,
% 0.09/0.36 % Sat Sep 26 03:14:12 2026
% 0.09/0.36 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.13/0.38
% 0.13/0.38 % From the command line: assign(max_seconds, 300).
% 5.23/1.15
% 5.23/1.15 % SZS status Theorem for theBenchmark
% 5.23/1.15
% 5.23/1.15 % Proof 1 at 0.63 (+ 0.06) seconds.
% 5.23/1.15 % Length of proof is 45.
% 5.23/1.15 % Level of proof is 10.
% 5.23/1.15 % Maximum clause weight is 29.000.
% 5.23/1.15 % Given clauses 326.
% 5.23/1.15
% 5.23/1.15 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------